Introductory Quantum Optics

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ISBN: 9780521820356 | 0521820359
Cover: Hardcover
Copyright: 11/22/2004

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This elementary introduction to the subject of quantum optics, the study of the quantum mechanical nature of light and its interaction with matter, is almost entirely concerned with the quantized electromagnetic field. The text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first- and second- year graduate students.

Acknowledgements

xii

1 Introduction

(9)

1.1 Scope and aims of this book

(1)

1.2 History

(5)

1.3 The contents of this book

(1)

References

(1)

Suggestions for further reading

(2)

2 Field quantization

(33)

2.1 Quantization of a single-mode field

(5)

2.2 Quantum fluctuations of a single-mode field

(2)

2.3 Quadrature operators for a single-mode field

(1)

2.4 Multimode fields

(7)

2.5 Thermal fields

(4)

2.6 Vacuum fluctuations and the zero-point energy

(4)

2.7 The quantum phase

(7)

Problems

(1)

References

(1)

Bibliography

(1)

3 Coherent states

(31)

3.1 Eigenstates of the annihilation operator and minimum uncertainty states

(5)

3.2 Displaced vacuum states

(2)

3.3 Wave packets and time evolution

(2)

3.4 Generation of coherent states

(1)

3.5 More on the properties of coherent states

(3)

3.6 Phase-space pictures of coherent states

(3)

3.7 Density operators and phase-space probability distributions

(6)

3.8 Characteristic functions

(6)

Problems

(1)

References

(1)

Bibliography

(1)

4 Emission and absorption of radiation by atoms

(41)

4.1 Atom-field interactions

(2)

4.2 Interaction of an atom with a classical field

(6)

4.3 Interaction of an atom with a quantized field

(5)

4.4 The Rabi model

(3)

4.5 Fully quantum-mechanical model; the Jaynes-Cummings model

(9)

4.6 The dressed states

(3)

4.7 Density-operator approach: application to thermal states

102

(3)

4.8 The Jaynes-Cummings model with large detuning: a dispersive interaction

105

(2)

4.9 Extensions of the Jaynes--Cummings model

107

(1)

4.10 Schmidt decomposition and von Neumann entropy for the Jaynes-Cummings model

108

(2)

Problems

110

(3)

References

113

(1)

Bibliography

114

(1)

5 Quantum coherence functions

115

(20)

5.1 Classical coherence functions

115

(5)

5.2 Quantum coherence functions

120

(4)

5.3 Young's interference

124

(3)

5.4 Higher-order coherence functions

127

(6)

Problems

133

(1)

References

133

(1)

Bibliography

134

(1)

6 Beam splitters and interferometers

135

(15)

6.1 Experiments with single photons

135

(2)

6.2 Quantum mechanics of beam splatters

137

(6)

6.3 Interferometry with a single photon

143

(1)

6.4 Interaction-free measurement

144

(2)

6.5 Interferometry with coherent states of light

146

(1)

Problems

147

(2)

References

149

(1)

Bibliography

149

(1)

7 Nonclassical light

150

(45)

7.1 Quadrature squeezing

150

(15)

7.2 Generation of quadrature squeezed light

165

(2)

7.3 Detection of quadrature squeezed light

167

(2)

7.4 Amplitude (or number) squeezed states

169

(2)

7.5 Photon antibunching

171

(1)

7.6 Schrödinger cat states

171

(11)

7.7 Two-mode squeezed vacuum states

182

(6)

7.8 Higher-order squeezing

188

(1)

7.9 Broadband squeezed light

189

(1)

Problems

190

(2)

References

192

(2)

Bibliography

194

(1)

8 Dissipative interactions and decoherence

195

(18)

8.1 Introduction

195

(1)

8.2 Single realizations or ensembles?

196

(4)

8.3 Individual realizations

200

(4)

8.4 Shelving and telegraph dynamics in three-level atoms

204

(3)

8.5 Decoherence

207

(1)

8.6 Generation of coherent states from decoherence: nonlinear optical balance

208

(2)

8.7 Conclusions

210

(1)

Problems

211

(1)

References

211

(1)

Bibliography

212

(1)

9 Optical test of quantum mechanics

213

(25)

9.1 Photon sources: spontaneous parametric down-conversion

214

(3)

9.2 The Hong-Ou-Mandel interferometer

217

(2)

9.3 The quantum eraser

219

(3)

9.4 Induced coherence

222

(2)

9.5 Superluminal tunneling of photons

224

(2)

9.6 Optical test of local realistic theories and Bell's theorem

226

(6)

9.7 Franson's experiment

232

(1)

9.8 Applications of down-converted light to metrology without absolute standards

233

(2)

Problems

235

(1)

References

236

(1)

Bibliography

237

(1)

10 Experiments in cavity QED and with trapped ions

238

(25)

10.1 Rydberg atoms

238

(3)

10.2 Rydberg atom interacting with a cavity field

241

(5)

10.3 Experimental realization of the Jaynes-Cummings model

246

(3)

10.4 Creating entangled atoms in CQED

249

(1)

10.5 Formation of Schrödinger cat states with dispersive atom-field interactions and decoherence from the quantum to the classical

250

(4)

10.6 Quantum nondemolition measurement of photon number

254

(1)

10.7 Realization of the Jaynes-Cummings interaction in the motion of a trapped ion

255

(3)

10.8 Concluding remarks

258

(1)

Problems

259

(1)

References

260

(1)

Bibliography

261

(2)

11 Applications of entanglement: Heisenberg-limited interferometry and quantum information processing

263

(31)

11.1 The entanglement advantage

264

(1)

11.2 Entanglement and interferometric measurements

265

(3)

11.3 Quantum teleportation

268

(2)

11.4 Cryptography

270

(1)

11.5 Private key crypto-systems

271

(2)

11.6 Public key crypto-systems

273

(1)

11.7 The quantum random number generator

274

(1)

11.8 Quantum cryptography

275

(6)

11.9 Future prospects for quantum communication

281

(1)

11.10 Gates for quantum computation

281

(5)

11.11 An optical realization of some quantum gates

286

(3)

11.12 Decoherence and quantum error correction

289

(1)

Problems

290

(1)

References

291

(2)

Bibliography

293

(1)

Appendix A The density operator, entangled states, the Schmidt decomposition, and the von Neumann entropy

294

(10)

A.1 The density operator

294

(3)

A.2 Two-state system and the Bloch sphere

297

(1)

A.3 Entangled states

298

(1)

A.4 Schmidt decomposition

299

(2)

A.5 von Neumann entropy

301

(1)

A.6 Dynamics of the density operator

302

(1)

References

303

(1)

Bibliography

303

(1)

Appendix B Quantum measurement theory in a (very small) nutshell

304

(4)

Bibliography

307

(1)

Appendix C Derivation of the effective Hamiltonian for dispersive (far off-resonant) interactions

308

(4)

References

311

(1)

Appendix D Nonlinear optics and spontaneous parametric down-conversion

312

(2)

References

313

(1)

Index

314

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Introductory Quantum Optics

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